The full rank condition for sparse random matrices

12/28/2021

∙

by   Amin Coja-Oghlan, et al.

∙

0

∙

share

We derive a sufficient condition for a sparse random matrix with given numbers of non-zero entries in the rows and columns having full row rank. The result covers both matrices over finite fields with independent non-zero entries and {0,1}-matrices over the rationals. The sufficient condition is generally necessary as well.